Finite difference method, Mathematics

Assignment Help:

2014_finite.png

Two reservoirs of equal cross sectional areas (315 m2) and at equal elevations are connected by a pipe of length 20 m and cross sectional area 3 m2. The reservoir on the left (reservoir 1) is filled with a liquid of mass density 1000 kg/m3. The pressure at the bottom of reservoir 1 (that is, p1) is 39000 N/m2. The second reservoir and the connecting pipe are initially empty. The acceleration due to gravity is 9.8 m/s2.

The following assumptions apply. One can ignore the effects of friction, form losses and the elevation differences along the path of the connecting pipe. The fluid is incompressible and inviscid. Flow through the connecting pipe is started by the instantaneous, full opening of the valve at the bottom of reservoir 1.

Using the finite difference method, write a Fortran program that predicts the behavior of the system for 200 seconds following the opening of the valve. Assume a timestep size of

0.1 sec. The program must read the above data (with the exception of the acceleration due to gravity and problem duration time of 200 seconds) from an input file and generate an output file. Run the following four cases;

a) one for the above data,

b) identical to case (a) but with the cross-sectional area of the second reservoir, A2, modified to 200 m2,

c) identical to case (a) but with the length of the connecting pipe, L, modified to 40 m, and

d) identical to case (a) but with the cross sectional flow area of the connecting pipe, Ap, modified to 6 m2.

The output file must include the following information:

Modeling and Simulation for Mechanical and Nuclear Engineers -

  • the date and time of the run,
  • a summary of the input data values, including units of measurement,
  • the maximum value of the volumetric flow rate, qv, through the connecting pipe(m3/s),
  • the maximum depths of the water in meters in each reservoir during the transient,
  • the maximum pressure at the exit of each reservoir (p1 and p2) during the transient (N/m2), and
  • a table of the volumetric flow rate through the connecting pipe (m3/s), the depth of water in each reservoir in meters, and the pressures p1 and p2 as a function of time.

The deliverables are:

  • the Fortran source code listing,
  • the input and output files for the four cases, and
  • the following plots as a function of time for each case:

the volumetric flow rate through the connecting pipe,

a comparison of the values of p1 and p2, and

a comparison of the fluid depth in each reservoir.

Plots should have appropriately labeled axes. The y-axis parameter value may be normalized if you wish.

In the text of the transmitting email answer the following:

1. explain the differences in the results of the four cases in terms of changes to the system's fluid capacitance Cf and fluid inductance If, and

2. Explain how this system relates to that of the unsteady flow in a U-tube discussed in class. For example, all else being equal, does the period of oscillation of the liquid in this system, like that of the U-tube system, vary as the square root of the length of the connecting pipe? Back up your answer either by reference to the required cases or to additional cases that you run.


Related Discussions:- Finite difference method

Tangents, two circle of radius of 2cm &3cm &diameter of 8cm dram common tan...

two circle of radius of 2cm &3cm &diameter of 8cm dram common tangent

Determine the matrix that performs a horizontal compression, (a) Determine ...

(a) Determine the matrix that first rotates a two-dimensional vector 180° anticlockwise, and then per- forms a horizontal compression of the resulting vector by a factor 1/2 (leavi

Exponential and logarithm equations, Exponential and Logarithm Equations ...

Exponential and Logarithm Equations : In this section we'll learn solving equations along with exponential functions or logarithms in them. We'll begin with equations which invol

What was the original price of the coat before tax, Nick paid $68.25 for a ...

Nick paid $68.25 for a coat, including sales tax of 5%. What was the original price of the coat before tax? Since 5% sales tax was added to the cost of the coat, $68.25 is 105%

Binomial theorem, use the expansion of (1-x)^7 to find the value of 1.998^7...

use the expansion of (1-x)^7 to find the value of 1.998^7 correct to five significant figures

Proof of various derivative facts formulas properties, PROOF OF VARIOUS DER...

PROOF OF VARIOUS DERIVATIVE FACTS/FORMULAS/PROPERTIES Under this section we are going to prove several of the different derivative facts, formulas or/and properties which we en

Write an equation in radius and solve it for radius, X and Y are centers of...

X and Y are centers of circles of radius 9cm and 2cm and XY = 17cm. Z is the centre of a circle of radius 4 cm, which touches the above circles externally.  Given that XZY=90 o , w

Normal approximation to binomial to approximate probability, A certain flig...

A certain flight arrives on time 78% of the time. Suppose 1000 flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that a)

Average, A boy covered half of distance at 20km/hr and rest at 40kmlhr. cal...

A boy covered half of distance at 20km/hr and rest at 40kmlhr. calculate his average speed.

What is the greatest value of the number, Five more than the quotient of a ...

Five more than the quotient of a number and 2 is at least that number. What is the greatest value of the number? Let x = the number. Notice that quotient is a key word for div

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd